I finally had time to check the link. I was not particularly impressed. For one thing, a single phase waveform goes to zero twice during a cycle, not three times. Also, three phase generation may be more efficient when powering three phase motors, but not necessarily when charging batteries through rectifiers. One should beware of generalizations. I also feel that some of the contributers misunderstand the basics. So, I thought I'd provide my take on this. Fell free to critique it.
For simplicity, suppose we start with 12 one inch diameter magnets and 12 coils. The coil size is not specified at this point except to say that the coil center hole is also one inch. We place the twelve magnets rather far apart relative to the coil size. As a coil moves across a north pole it produces a positive voltage pulse followed immediately by a negative voltage pulse and then a time of no voltage. Continuing over the following south pole it produces a negative pulse, a positive pulse, and a time of zero voltage. If the magnets are brought closer together one can eliminate the times of zero voltage. However, that still leaves a peculiar voltage waveform that goes ++,--,++,--,... While one could probably use it, a better solution would be to bring the magnets still closer until the dual pulses combine into one pulse of greater voltage. Well, the closest you can bring the magnets is determined by the coil size. The sum of the magnet diameter plus the magnet spacing can be no less than the coil diameter. For instance two inch diameter coils allow for a one inch magnet spacing. When a coil and magnet align the voltage induced in the coil is zero even though the flux is maximum. When the coil is exactly centered over two adjacent magnets the flux through it will be zero. However, the flux will then be changing at a maximum rate yielding the maximum voltage. Half the coils will be producing positive pulses and half will be producing negative pulses, which can be grouped and connected to produce a single phase output. The output voltage will be the sum of the voltages of the 12 coils acting in phase.
If we now wish to use the same coils and magnets for a three phase alternator we start by throwing away three coils. One would then normally move the magnets closer together so that the coils touch and that they overlap the magnets as much as possible when centered between two adjacent magnets. A greater overlap will result in a greater induced voltage if the speed at which the magnets pass the coils doesn't change. With the magnets closer together it does change, since a smaller diameter rotor would be used. It's not clear that the peak voltage will actually increase. It is clear that the average voltage will be the same in both cases. The average voltage for a coil is given by the change in flux as the coil moves from magnet center to following magnet center divided by the time it takes. At the same RPM with 12 equally spaced magnets the time to move 30 degrees is the same for both the single phase and the three phase alternators. The change in flux is also the same, as the coils and magnets are the same in both cases. At this point it should be clear that in the voltage sweepstakes the single phase will likely win, since it is getting its output from 12 in phase coils rather than two groups of three which are slightly out of phase of each other.
Another factor is alternator resistance. The single phase will exhibit twice the resistance than the three phase. This will affect power output.